Which of the following equations represents an ellipse with a minor axis of length 10 and foci located at (3,6) and (7,6)?
Answers
Answer:
It is choice A.
Step-by-step explanation:
The general form is (x - h)^2 / a^2 + (x - k)^2/b^2 = 1 where (h, k) is the center, 2a = major axis and 2b = minor axis.
The ellipse in the question has a^2 > b^2 so the major axis is parallel to the x axis.
The minor axis which is parallel to the y-axis is of length 10 so b^2 = (1/2 * 10)^2
= 25 so we can eliminate C.
The center of the ellipse = the midpoint of a line joining the focii so it is:
( 3+ 7)/2, 6)
= (5,6).
As (h, k) is the center we have h = 5 and k = 6.
So it is choice A.
The equation of the eclipse will be [tex]\frac{(x-5)^2}{29} +\frac{(y-6)^2}{25} =1[/tex] i.e. option A.
What is equation of the ellipse?The standard equation of the ellipse is [tex]\frac{(x-h)^2}{a^2} +\frac{(y-k)^2}{b^2} =1[/tex].
Here,
(h, k) is the center, and 2a and 2b are major and minor axis.
We have,
Length of minor axis = 10
i.e. 2b = 10
And, b = 5
And,
Foci (c) located at (3,6) and (7,6),
i.e. Major axis is parallel to x-axis. [Because y is constant]
And,
The foci (c) always lie on the major axis.
And,
c² = a² - b²
Now,
The center of an ellipse is the midpoint of both the major and minor axes, i.e. the midpoint of a line joining the foci (c),
i.e. Center [tex]=( \frac{x_1 + x_2 }{2}, \frac{y_1 + y_2}{2}) =( \frac{3+7}{2}, \frac{6+6}{2}) =(5, 6)[/tex]
Now,
Foci (c) = 5 - 3 = 2
So,
c² = a² - b²
i.e.
2² = a² - 5²
4 = a² - 25
⇒ a² = 29
And, b² = 5² = 25
So,
h = 5 and k = 6
Now,
Putting the values in the standard form of equation of the ellipse,
i.e.
[tex]\frac{(x-h)^2}{a^2} +\frac{(y-k)^2}{b^2} =1[/tex]
i.e.
[tex]\frac{(x-5)^2}{29} +\frac{(y-6)^2}{25} =1[/tex]
So, this is the equation of the eclipse i.e. option A.
Hence, we can say that the equation of the eclipse will be [tex]\frac{(x-5)^2}{29} +\frac{(y-6)^2}{25} =1[/tex] i.e. option A.
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Related Questions
Cam bought some used books for $4.95. He paid $0.50 each for some books and $0.35 each for the others. He bought fewer than 8 books at each price. How many books did Cam buy?
Answers
Answer:
cam bought 12 books 7 at $0.35 and 5 at $0.50
Step-by-step explanation:
Perform the following calculation: 1.9 + 6.25 =
Answers
Answer:
8.15
Step-by-step explanation:
Step-by-step explanation:
1.9+6.25=8.15
1.9
+ 6.25
______
8.15
Select the correct answer
An air conditioning unit promises to have a cooling capacity of 6,000 British thermal units (Btu). The unit has a maximum variance of y Btu. If x is the
air conditioning unit's actual capacity, which graph could be used to determine variance levels that would cause a unit to be rejected because of its
cooling capacity?
(A,B,C,D)
Answers
Answer:
the answer will 100 percent be A
Answer:
The correct option is B.
Step-by-step explanation:
Let x is the air conditioning unit's actual capacity and y is the maximum variance in British thermal units (Btu).
It is given that an air conditioning unit promises to have a cooling capacity of 6,000 British thermal units (Btu).
It means the maximum variance is less than or equal to absolute difference of actual capacity and 6,000.
[tex]y\leq |x-6000|[/tex]
The related equation of this inequality is a V-shaped curve with vertex (6000,0) and y-intercept (0,6000). Related curve is a solid curve because the points on curve included in the solution set.
The shaded region lie below the curve because the sign of inequality is ≤.
Therefore the correct option is B.
Carrie spent 1/4 of her allowance on a shirt 1/3 of her allowance Oscar and eight dollars on the bill if she spent 22 in all how much was Carrie’s allowance
Answers
Answer: $24
Step-by-step explanation:
Let x represent the amount of Carrie's allowance.
[tex]\dfrac{1}{4}x+\dfrac{1}{3}x+8=22\\\\\\\dfrac{1}{4}x+\dfrac{1}{3}x=14\\\\\\(12)\dfrac{1}{4}x+(12)\dfrac{1}{3}x=(12)14\\\\\\3x + 4x = (12)14\\\\\\7x=(12)14\\\\\\x=(12)2\\\\\\x=24[/tex]
What are the x-intercepts of the graph of the function f(x) = x2 + 5x − 36?
Answers
Answer:(4,0) and (-9,0)
Step-by-step explanation:
Find two numbers their product will be -36 when you add those two numbers together your sum will be 5
-4(9) = -36
-4 + 9 = 5
So
(X-4)(x+9)
X-4= 0
X= 4
X+9=0
X= -9
The x-intercept are (4,0) and (-9,0)
Hope this helps!
The width of rectangular field is x metres.
The length of the field is 30m longer than the width.
The perimeter of the field is less than 500m.
The area of the field is greater than 4000m^2
By writing suitable inequalities, find the possible values of x
Answers
Answer:
Possible values of x are 50 < x < 110.
Step-by-step explanation:
Consider the perimeter of the field:
2x + 2(x + 30) < 500
2x + 2x + 60 < 500
4x < 440
x < 110.
Consider the area of the field:
x(x + 30 ) > 4000
x^2 + 30x - 4000 > 0
(x - 50)(x + 80) > 0
The critical values are x = -80 and 50.
As x is a width it must be positive so x > 50.
Use the elimination method to find the solution to the system of equations. 2x - 3y = -9 -x + 3y = 6
Answers
Answer:
x = -3, y = 1 → (-3, 1)Step-by-step explanation:
[tex]\underline{+\left\{\begin{array}{ccc}2x-3y=-9\\-x+3y=6\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad x=-3\\\\\text{put the value of x to the second equation:}\\\\-(-3)+3y=6\\3+3y=6\qquad\text{subtract 3 from both sides}\\3y=3\qquad\text{divide both sides by 3}\\y=1[/tex]
What is the quotient?
Answers
Answer:
4 x [tex]10^{12}[/tex])
Step-by-step explanation:
(6 x [tex]10^{8}[/tex]) / (1.5 x [tex]10^{-4}[/tex])
= ([tex]\frac{6}{1.5}[/tex] x [tex]10^{8}[/tex]) / ([tex]10^{-4}[/tex])
= ([tex]\frac{6}{1.5}[/tex] x [tex]10^{8}[/tex]) x ([tex]10^{4}[/tex])
= [tex]\frac{6}{1.5}[/tex] x [tex]10^{12}[/tex]
= 4 x [tex]10^{12}[/tex]
Step-by-step explanation:
6*10^8 /1.5*10^-4
6/1.5 * 10^8/10^-4
4 * 10^8-(-4)
4*10^8+4
4*10^12
plz answer asap i need to graduate this week
UNIT 3 REVIEW
Circle the correct answer to each of the following questions. All
answers are rounded to the second decimal place,
1. What is the volume of a building that is 18 meters long,
9 meters wide, and 6 meters high?
a. 948 meters b. 972 meters c. 984 meters
2. What is the volume of a fish tank that is 26 inches long,
14 inches wide, and 18 inches high?
a. 6552 inches b. 6844 inches 7208 inches
3. What is the volume of a cube with dimensions that are each
7.2 feet long?
a. 51.84 feet b. 373.25 feet c 2686.39 feet
4. What is the volume of a cube with dimensions that are each
4.5 yards long?
a. 20.25 yards' b. 67.29 yards' C 91.13 yards
Answers
Question 1:
For this case we have that by definition, the volume of a prism is given by:
[tex]V = a * b * c[/tex]
Where:
a: It is the long
b: It is the width
c: It is the height
According to the data we have:
[tex]a = 18m\\b = 9m\\c = 6m[/tex]
Substituting:
[tex]V = 18 * 9 * 6\\V = 972[/tex]
Thus, the volume of the building is[tex]972 \m ^ 3[/tex]
Answer:
Option B
Question 2:
For this case we have that by definition, the volume of a prism is given by:
[tex]V = a * b * c[/tex]
Where:
a: It's the long
b: It is the width
c: It is the height
According to the data we have:
[tex]a = 26in\\b = 14in\\c = 18in[/tex]
Substituting:
[tex]V = 26 * 14 * 18\\V = 6552[/tex]
Thus, the volume of the tank is [tex]6552 \in ^ 3[/tex]
Answer:
Option A
Question 3:
For this case we have that by definition, the volume of a cube is given by:
[tex]V = l ^ 3[/tex]
Where:
l: It's the side of the cube
According to the data we have that the cube side is 7.2ft.
Substituting we have:
[tex]V = (7.2) ^ 3\\V = 373.25[/tex]
Rounding off we have that the volume of the cube is [tex]373.25 \ ft ^ 3[/tex]
Answer:
Option B
Question 4:
For this case we have that by definition, the volume of a cube is given by the following formula:
[tex]V = l ^ 3[/tex]
Where:
l: It's the side of the cube
According to the data we have that the cube side is 4.5 yards.
Substituting we have:
[tex]V = (4.5) ^ 3\\V = 91.125[/tex]
Rounding off we have the cube volume is[tex]91.13 \ yd ^ 3[/tex]
Answer:
Option C
I need this explained
Answers
[tex]\text{Hey there!}[/tex]
[tex]\text7x}^2\text{- 32x - 60}[/tex]
[tex]\text{The answer is: (7x + 10)(x - 6)}[/tex]
[tex]\text{Because if you follow the step to the answer (first you have to distribute}[/tex] [tex]\text{then combine the like terms after distributing) after all of that you SHOULD}[/tex] [tex]\text{get the equation back!}[/tex]
[tex]\text{Distribute}\downarrow\\\\\text{7x(x)=7x}^2\\ \text{7(-6x)= -42}\\\text{10(x)= 10x}\\\text{10(-6)= -60}[/tex]
[tex]\text{Combine your like terms (terms that has the almost the same thing)}\downarrow[/tex]
[tex]\text{-42x + 10x = -32x}[/tex]
[tex]\text{The other terms stays the same because they DON'T have like terms}[/tex]
[tex]\text{Original problem: 7x}^2\text{- 32x -60}[/tex]
[tex]\boxed{\boxed{\bf{Answer: (7x+10(x -6))}}}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
Help me pleasseeeeeeeeeeeeee
Answers
Answer:
A. x ≤ 0Step-by-step explanation:
Look at the picture.
The range: -6 ≤ y ≤ 9
The domain: x ≤ 0
If 5x−2y=10 and x= 4y/5 , then y =
(A) 1 (B) 4 (C) 5 (D) 7 (E) 9
Answers
Answer:
C
Step-by-step explanation:
4y-2y=10
y=5
For the function, f(x) = -5x 2, find f(-4).
Answers
Answer:
The value of f(-4) = -80
Step-by-step explanation:
It is given that, f(x) = -5x²
To find the value f(-4)
Let f(x) = -5x²
To find the value of f(-4), substitute -4 instead of x
f(-4) = -5 * (-4)²
= -5 * 16 [ since (-4)² = -4 * -4 = 16 ]
= -80
Therefore the value of f(-4) = -80
a sequence is a function whose domain is the set of _____ numbers
Answers
a sequence is a function whose domain is the set of natural numbers.
natural numbers are all the negative and positive integers
A sequence exists as a function whose domain is the set of natural numbers.
SequenceA sequence exists as a function whose domain is the set of natural numbers or a subset of the natural numbers. Usually use the symbol a to describe a sequence, where n is a natural number and a stands for the value of the function on n. Intuitively, a sequence exists just as an ordered list of (possibly infinitely many) numbers.
Natural numbers stand for the numbers that exist used for counting and are a part of real numbers.A sequence exists as an enumerated collection of objects in which repetitions are permitted and order matters.To learn more about Sequence refer to:
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Using the given points and line, determine the slope of the line. (-3, 0) and (2, 7) slope = -7/5
slope = -5/7
slope = 5/7
slope = 7/5
Answers
Answer:
Slope= 7/5
Step-by-step explanation:
The slope of a line is determined as a ratio of the change in y to the change in x.
Slope=Δy/Δx
Δy=y₂-y₁
Δx=x₂-x₁
Therefore we can use the the x and y coordinates from the points given, (-3,0) and (2,7) to calculate the slope.
m= (7-0)/(2-⁻3)
Slope= 7/5
When a negative number is subtracted from a number it the operation sign changes to addition.
Answer: Last option
[tex]slope=\frac{7}{5}[/tex]
Step-by-step explanation:
The equation to find the slope m of a line is:
[tex]m=\frac{y_2-y_2}{x_2-x_1}[/tex]
Where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are two points through which the line passes
In this case the points are: (-3, 0) and (2, 7)
Therefore the slope is:
[tex]m=\frac{7-0}{2-(-3)}[/tex]
[tex]m=\frac{7}{2+3}[/tex]
[tex]m=\frac{7}{5}[/tex]
The answer is the last option
anisha is graphing the function f(x) = 25(3/5)x. She begins by plotting the point (1, 15). Which could be the next point she plots on the graph? (2, 9) (2, –10) (2, 14) (2, 5)
Answers
Answer:
(2, 9)
Step-by-step explanation:
We've been given the exponential function;
f(x) = 25(3/5)^x
We need to determine the value of f(x) when x = 2, that is;
f(2) = 25(3/5)^2
Using a calculator we obtain
f(2) = 9
Thus the next point she plots on the graph will be (2, 9)
Consider the following proportion:
2/7 =
12x
Use cross products to write the equation: 2x = 84.
What is the value of x?
Answers
Answer:
x=42
Step-by-step explanation:
2x42
Answer:
42
Step-by-step explanation:
tell me if i am wrong by reporting
what is -4/3 in a fraction that isn't improper
Answers
Answer:
-1 1/3
Step-by-step explanation:
To change and improper fraction (larger number in the numerator than the denominator) to a mixed number
divide the numerator by the denominator
4/3 =1 with 1 left over
Take the leftovers and put it over the denominator
1/3
The mixed number is 1 1/3
Since the number was negative, we put the negative out front
-1 1/3
the difference between maggies age and terrance age is 3. if x represents maggies age and y represents terrance age, make a table of possible values for x and y. graph the ordered pair and describe the graph
Answers
Step-by-step explanation:
There can be two situations
1. When maggie is older
The equation becomes x = y + 3
It can also be expressed as y = x - 3
2. When maggie is younger
The equation becomes y = x + 3
Table of possible values
1. x y 2. x y
5 2 2 5
6 3 3 6
Answer:
The required equation is [tex]|y-x|=3[/tex]. If maggies is elder, then [tex]y_1=x-3[/tex] and if maggies is younger, then [tex]y_2=x+3[/tex].
Step-by-step explanation:
Let the x represents maggies age and y represents terrance age, make a table of possible values for x and y.
It is given that the difference between maggies age and terrance age is 3.
It means
[tex]|y-x|=3[/tex]
On simplification, we get
[tex]y-x=\pm 3[/tex]
[tex]y=x\pm 3[/tex]
Case 1: If maggies is elder.
[tex]y_1=x-3[/tex]
Case 2: If maggies is younger.
[tex]y_2=x+3[/tex]
The table of values is
x y₁ y₂
-3 -6 0
0 -3 3
3 0 6
The graph of both functions are shown below.
Can you help with this please?
[tex]2n \times n = 12 + n[/tex]
Answers
Answer:
2n² = 12 + n
2n² - n - 12 = 0
[tex]n = \frac{1 ± \sqrt{ {( - 1)}^{2} - 4(2)( - 12)} }{2(2)} [/tex]
[tex]n = \frac{1 ± \sqrt{97} }{4} [/tex]
Determine the factors of x2 − 12x − 20.
Answers
Answer:
(x-10)(x-2)
Formula:
a^{2} - b^{2} = (a-b)(a+b)
Explanation:
(x-6)^2-4^2
Then we can simplify to, (x-6-4)(x-6+4)
Which comes to your answer, (x-10)(x-2)
Answer:
Step-by-step explanation:
x² − 12x − 20 = 0
a = 1; b = (-12); c = (-20)
b²-4ac = (-12)² - 4 * 1 * (-20) = 144 + 80 = 224
√b²-4ac = √ 224 = √ 2*2*2*2*2*7 = 2*2*√(2*7) = 4√14
delta = -b ± √b²-4ac / 2a
= -(-12) ± 4√14
2 * 1
= (12 ± 4√14)/2
= 2 ( 6 ± 2√14) / 2
= 6 ± 2√14
x = 6 + 2√14; x = 6 - 2√14
Factor the polynomial: -x^3-3x^2-4x
Answers
Answer:
-x(x^2 +3x +4)
Step-by-step explanation:
-x^3-3x^2-4x
Factor out a -x
-x(x^2 +3x +4)
We cannot factor inside the parentheses, so this is complete
Which expression is equal too |-12| -|3|
Answers
Answer:
9
Step-by-step explanation:
12 - 3 = 9
Hello :D
Answer:
[tex]\boxed{9}\checkmark[/tex]
The answer has a positive sign.
Step-by-step explanation:
Order of operations
PEMDAS
Parenthesis
Exponents
Multiply
Divide
Add
Subtract
Left to right
[tex]|-12|-|3|[/tex]
[tex]12-3=9[/tex]
[tex]\boxed{9}[/tex], which is our answer.
Hope this helps! :D
Match each equation to the value of a that makes the equation true.
2a + 3(a + 1) = 8
2
4
0
1
3
Answers
Answer:
a=1
Step-by-step explanation:
2a + 3(a + 1) = 8
Distribute
2a +3a +3 = 8
Combine like terms
5a +3 =8
Subtract 3 from each side
5a+3-3=8-3
5a = 5
Divide by 5
5a/5 = 5/5
a=1
1/2x = -40
What is x?
Answers
Answer:
x = -80
Explanation
-40 divided by 1/2 is -80
that is you’re answer because -40 and x2 is -80
What’s 120% of 200?
Please Help
Answers
Answer:
240
Step-by-step explanation:
200 divided by 100, to get the amount per percent, then multiply it by 120, to get 240.
Answer:
Step-by-step explanation:200 multipled by 120%
200 • 120/100
Reduce the numbers with the greatest common divisor 100
2 • 100
2 •120
Multiply the numbers
THE ANSWER IS 240
Suppose cluster sampling were being used to survey MyBook users, who
amount to 28% of the population of the United States. Based on the table
below, which city would be considered the best cluster?
Denver 27%
Honolulu 9%
Miami 16%
Philadelphia 46%
A. Philadelphia
B. Miami
C. Denver
D. Honolulu
Answers
Answer:
The best cluster would be Philadelphia which percentage of 27% is nearly close to 28% of the whole united states population percentage.
Step-by-step explanation:
The correct option for the city which would be considered as the best cluster is B. Miami, 16% of the population are MyBook users.
What is a survey?A survey is a means of gathering information from a sample of people using pertinent questions with the goal of understanding populations as a whole.
Now given that,
Amount of population that are MyBook users = 28%
Thus,
Amount of population that do not uses MyBook = 100% - 28% = 72%
Thus, Philaldephia and Denver cannot be percentage of the population who are MyBook users.
Thus, the correct option for the city which would be considered as the best cluster is B. Miami, 16% of the population are MyBook users.
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Select the correct answer. Will is at a shirt sale where he can buy one and get a second one for 40 percent off. He wants to buy two shirts priced at $29 each. How much will he pay? cost after discount = (2 × list price) – (list price × discount percentage) A. $34.80 B. $40.60 C. $46.40
Answers
Answer:
C
Step-by-step explanation:
Givens
Original cost = 29 dollars.
Discount = 40% on the second shirt.
Formula
cost after discount = (2 × list price) – (list price × discount percentage)
Solution
Cost after discount = 2 * 29 - 29*40/100
Cost after discount = 58 - 11.60
Cost after discount = 46.40
Find the product.
(a^2-b)(5a^2+6b)
Answers
F (first) = a^2 * 5a^2 = 5a^4
I (inner) = -b * 5a^2 = -5a^2b
O (outer) = a^2 * 6b = 6a^2b
L (last) = 6b * -b = -6b^2
All that is left is to combine and simplify (is possible):
5a^4 -5a^2b + 6a^2b -6b^2
5a^4 + a^2b -6b^2
The final answer for this problem is:
5a^4 + a^2b -6b^2
Hope this helps!
Answer:
[tex]( {a}^{2} - b)(5 {a}^{2} + 6b) \\ 5 {a}^{4} + 6 {a}^{2} b - 5 {a}^{2} b - 6 {b}^{2} \\ = 5 {a}^{4} + {a}^{2} b - 6 {b}^{2} [/tex]
How is solving for speed similar to solving for time?
Answers
Speed = distance/time
Time= distance/ speed
So basically distance divided both of them when they find speed distance divide time when fine time distance divide speed.
Hope this helps!
Time= distance/speed (T = d/s)
Rate or speed are similar since they both represent some distance per unit time such miles per hour and kilometers per hour. To solve for time use the formula for time, t = d/s which means time equals distance divided by speed.
What is the formula for distance divided by time?distance = rate x time To solve for speed or rate use the formula for speed, s = d/t which means speed equals distance divided by time.
What is the relationship between speed and time?This is because, speed of the object refers distance travelled divided by time or it expressed as, Furthermore, 1 could also explain the relationship of the time with other two variables using this formula. Speed could be of 2 types, relative or average.
from the formula,
Distance = time * speed
Speed = distance/time
Time= distance/speed (T = d/s)
So basically distance divided both of them when it find speed distance divide time when fine time distance divide speed.
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